In the hitherto known combustion systems of this type, the vibratory combustion bed consists of a plurality of hollow stepped profile sections which are constructed in the form of stairs and are secured to a vibratory frame, the air of combustion being supplied to the upper part of the vibratory combustion bed through the nozzle openings existing between neighboring stepped profile sections. Such systems can be improved to obtain better performance which is limited due, on the one hand, to problems of casting technology and, on the other hand, to reasons of vibration technology. A bed of the type to which this invention relates is shown in U.S. Pat. No. 3,791,316, by the inventor hereof.